From time to time we need to remove all the items out of the Office 365 search index. There are 3 options:
1. Re-index everything on premises and after the indexing completes delete the content sources to trigger a delete crawl to run. Of course re-indexing everything is not efficient, it takes time and if items have been deleted from the on premises content you still run the risk of missing orphans in the Office 365 search index.
2. Call Microsoft Office 365 support and raise a ticket to ask for an index purge, something that takes time and again is inefficient for the task at hand.
3. Use DeleteAllCloudHybridSearchContent method of PushTenantManager.
That was another page in the Chronicles of SharePoint Bits, happy scripting!